Do these ratios form a proportion?

A right triangle has a hypotenuse length of 13 units. One leg has a length of 12 units. Which equation can be used to determine

viktelen [127]

a = √(13² - 12²) units

<h3>Further explanation</h3>

<u>Given:</u>

A right triangle has a hypotenuse length of 13 units.
One leg has a length of 12 units

<u>Question:</u>

Which equation can be used to determine the length of the other leg?

<u>The Process:</u>

We will solve a problem regarding right triangles. In the process, there is a relationship between the Pythagorean Theorem with Exponent and Square Root.

Let us find out the equation to determine the length of the other leg. Let the length of the leg as "a".

The Phytagorean Theorem:

$\boxed{ \ (leg)^2 + (leg)^2 = (hypotenuse)^2 \ }$

$\boxed{ \ a^2 + 12^2 = 13^2 \ }$

Subtract by 12² on both sides.

$\boxed{ \ a^2 = 13^2 - 12^2 \ }$

To take the square root on both sides.

So here's the equation that can be used to determine the length of the other leg: $\boxed{\boxed{ \ a = \sqrt{13^2 - 12^2} \ }}$

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Notes

If we continue working on the above, the results will be as follows:

$\boxed{ \ a = \sqrt{13^2 - 12^2} \ }$

$\boxed{ \ a = \sqrt{169 - 144} \ }$

$\boxed{ \ a = \sqrt{25} \ }$

Hence the length of the other leg equal to a = 5 cm.

Of course, we agree with the use of the right intuition, which is to remember Pythagorean Triples, i.e., $\boxed{ \ 5-12-13 \ }.$ This method is very convenient when working on multiple-choice tests in a limited amount of time.

<h3>Learn more</h3>

What are the lengths of the legs of the triangle? brainly.com/question/13027296
Find out the measures of the two angles in a right triangle brainly.com/question/4302397
A word problem of a quadratic equation brainly.com/question/11805547

5 0

4 years ago

Riemann Hypothesis: Explain how to answer it ( hardest math problem in the world)

bija089 [108]

Answer:

Addicts the remote hypothesis is a conjecture that the remote data function has it zeroes only at the negative even integers in complex numbers with real part half many considered to be the most important unsolved problem in pure mathematics is of great interest in number theory because it implies results about the distribution of prime numbers

5 0

3 years ago

What coordinate for F would make triangle ABC and triangle DEF congruent? (The file of the image is attached!)

DerKrebs [107]

(-2,-3) would make these two triangles congruent.

If you look at the slope of line DE, you see it has a -1 slope.
Line BA also has a -1 slope.
So line AC = line FE and line BC = line FD

The slope of AC is 3
The slope of BC is 1/3
Two possible points for F are (2,1) and (-2,-3)
Since (2,1) is not an option, C. (-2,-3) is your answer.

5 0

3 years ago

Read 2 more answers

Rewrite in simplest rational exponent form square root of x times the fourth root of x. Show each step of your process.

belka [17]

Answer:

$\sqrt[4]{ {x}^{3} }$

Step-by-step explanation:

$\sqrt{x} \times \sqrt[4]{x} \\ = {x}^{ \frac{1}{2} } \times {x}^{ \frac{1}{4} } \\ = {x}^{ \frac{1}{2} + \frac{1}{4} } \\ = {x}^{ \frac{3}{4} } \\ = \sqrt[4]{ {x}^{3} }$